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Examples of exponentially many collisions in a hard ball system

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  23 October 2020

DMITRI BURAGO  and
SERGEI IVANOV
DMITRI BURAGO
Affiliation:
The Pennsylvania State University, Department of Mathematics, University Park, PA16802, USA (e-mail: burago@math.psu.edu)
SERGEI IVANOV
Affiliation:
St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia (e-mail: svivanov@pdmi.ras.ru)
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Abstract

Consider the system of n identical hard balls in ${\mathbb {R}}^3$ moving freely and colliding elastically. We show that there exist initial conditions such that the number of collisions is exponential in n.

Keywords

hard ball gas modelnumber of collisionsexamples with many collisions

MSC classification

Primary: 37D50: Hyperbolic systems with singularities (billiards, etc.)
Secondary: 70F35: Collision of rigid or pseudo-rigid bodies
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 9 , September 2021 , pp. 2754 - 2769
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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